We present a predictive method that can simulate an essential step in the antigen presentation in higher vertebrates, namely the step involving the proteasomal degradation of polypeptides into fragments which have the potential to bind to MHC Class I molecules. Proteasomal cleavage prediction algorithms published so far were trained on data from in vitro digestion experiments with constitutive proteasomes. As a result, they did not take into account the characteristics of the structurally modified proteasomes--often called immunoproteasomes--found in cells stimulated by gamma-interferon under physiological conditions. Our algorithm has been trained not only on in vitro data, but also on MHC Class I ligand data, which reflect a combination of immunoproteasome and constitutive proteasome specificity. This feature, together with the use of neural networks, a non-linear classification technique, make the prediction of MHC Class I ligand boundaries more accurate: 65% of the cleavage sites and 85% of the non-cleavage sites are correctly determined. Moreover, we show that the neural networks trained on the constitutive proteasome data learns a specificity that differs from that of the networks trained on MHC Class I ligands, i.e. the specificity of the immunoproteasome is different than the constitutive proteasome. The tools developed in this study in combination with a predictor of MHC and TAP binding capacity should give a more complete prediction of the generation and presentation of peptides on MHC Class I molecules. Here we demonstrate that such an approach produces an accurate prediction of the CTL the epitopes in HIV Nef. The method is available at www.cbs.dtu.dk/services/NetChop/.